<p><b>Abstract</b>—In this paper, we propose a generalized approach for designing a class of dynamic hashing schemes which require no index and have the growth of a file at a rate of</p><tf>$${\textstyle{{n\,+\,1} \over n}}$$</tf><ip1>per full expansion, where <it>n</it> is the number of pages of the file, as compared to a rate of two in linear hashing. Based on this generalized approach, we derive a new dynamic hashing scheme called <it>alternating hashing</it>, in which, when a split occurs in page <it>k</it>, the data records in page <it>k</it> will be redistributed to page <it>k</it> and page (<it>k</it> + 1), or page <it>k</it> and page (<it>k</it>− 1), according to whether the value of <it>level d</it> is even or odd, respectively. (Note that a <it>level</it> is defined as the number of full expansions happened so far.) From our performance analysis, given a fixed load control, the proposed scheme can achieve nearly 97% storage utilization as compared to 78% storage utilization by using linear hashing.</ip1>